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統計力學 第2版 英文

為了解決Gibbs free energy un的問題，作者(美)馬提斯 這樣論述：

《統計力學(第2版)》在第一版的基礎上做了大量的擴展和改進，廣受好評。對統計概念的原始講述，使得《統計力學(第2版)》對理論物理的發展產生了深刻的影響，並且為現代熱動力學觀點的形成奠定了基礎。 Preface to Second Edition Preface to First Edition Introduction: Theories of Thermodynamics, Kinetic Theory and Statistical Mechanics Chapter 1 Elementary Concepts in Statistics and Probabilit

y 1.0. Random Variables and Their Distributions 1.1. The Binomial Distribution 1.2. Length of a Winning Streak 1.3. Brownian Motion and the Random Walk 1.4. Poisson versus Normal (Gaussian) Distributions 1.5. Central Limit Theorem (CLT) 1.6. Multinomial Distributions, Statistical Thermodynamics 1.7.

The Barometer EquatiOn 1.8. Other Distributions Chapter 2 The Ising Model and the Lattice Gas 2.0. Physical Applications of the Binary Model 2.1. Some Background and Motivation 2.2. First-Principles Statistical Theory of Paramagnetism 2.3. More on Entropy and Energy 2.4. Some Other Relevant Thermo

dynamic Functions 2.5. Mean-Field Theory, Stable and Metastable Solutions 2.6. The Lattice Gas 2.7. The Nearest-Neighbor Chain: Thermodynamics in 1D 2.8. The Disordered Ising Chain 2.9. Other Magnetic Systems in One Dimension Chapter 3 Elements of Thermodynamics 3.1. The Scope of Thermodynamics 3.2

. Equations of State and Some Definitions 3.3. Maxwell Relations 3.4. Three Important Laws of Thermodynamics 3.5. The Second Derivatives of the Free Energy 3.6. Phase Diagrams for the van der Waals Gas 3.7. Clansius-Clapeyron Equation 3.8. Phase Transitions 3.9. The Carnot Cycle 3.10. Superconductiv

ity Chapter 4 Statistical Mechanics 4.0. An Axiomatic Approach and the Ergodic Hypothesis 4.1. The Formalism -- and a False Start 4.2. Gibbs' Paradox and Its Remedy 4.3. The Gibbs Factor 4.4. The Grand Ensemble 4.5. Non-Ideal Gas and the 2-Body Correlation Function 4.6. The Virial Equation of State

4.7. Weakly Non-Ideal Gas 4.8. Two-body Correlations 4.9. Configurational Partition Function in 1D 4.10. One Dimension versus Two 4.11. Two Dimensions versus Three: The Debye--Waller Factors 4.12. Specific Heat of Quasi-Ideal Dilute Atomic and Diatomic Gases 4.13. Nanophysics and Inhomogeneity Cha

pter 5 The World of Bosons 5.0. Quantum ""Statistics"" 5.1. Two Types of Bosons and Their Operators 5.2. Number Representation and the Many-Body Problem 5.3. The Adiabatic Process and Conservation of Entropy 5.4. Many-Body Perturbations 5.5. Photons 5.6. Phonons 5.7. Ferromagnons 5.8. Conserved Boso

ns and the Ideal Bose Gas 5.9. Nature of ""Ideal"" Bose-Einstein Condensation 5.10. Ideal Bose-Einstein Condensation in Low Dimensions 5.11. Consequences of a Hard Core Repulsion in 1D 5.12. Bosons in 3D Subject to Weak Two-Body Forces 5.13. Superfluid Helium (He Ⅱ) Chapter 6 All About Fermions: Th

eories of Metals, Superconductors, Semiconductors 6.1. Fermi-Dirac Particles 6.2. Slater Determinant: The Ground State 6.3. Ideal Spinless Fermi-Dirac Gas 6.4. Ideal Fermi-Dirac Gas with Spin 6.5. Fermi Integrals 6.6. Thermodynamic Functions of an Ideal Metal 6.7. Quasiparticles and Elementary Excit

ations 6.8. Semiconductor Physics: Electrons and Holes 6.9. n-Type Semiconductor Physics: The Statistics 6.10. Correlations and the Coulomb Repulsion 6.11. Miscellaneous Properties of Semiconductors 6.12. Aspects of Superconductivity: Cooper Pairs 6.13. Aspects of BCS Theory 6.14. Contemporary Devel

opments in Superconductivity Chapter 7 Kinetic Theory 7.1. Scope of This Chapter 7.2. Quasi-Equilibrium Flows and the Second Law 7.3. The Collision Integral 7.4. Approach to Equilibrium of a ""Classical"" Non-Ideal Gas 7.5. A New Look at ""Quantum Statistics"" 7.6. Master Equation: Application to R

adioactive Decay 7.7. Boltzmann Equation 7.8. Electrical Currents in a Low-Density Electron Gas 7.9. Diffusion and the Einstein Relation 7.10. Electrical Conductivity of Metals 7.11. Exactly Solved ""Backscattering"" Model 7.12. Electron-Phonon Scattering 7.13. Approximating the Boltzmann Equation 7

.14. Crossed Electric and Magnetic Fields 7.15. Propagation of Sound Waves in Fluids 7.16. The Calculations and Their Result Chapter 8 The Transfer Matrix 8.1. The Transfer Matrix and the Thermal Zipper 8.2. Opening and Closing a ""Zipper Ladder"" or Polymer 8.3. The Full Zipper (N > 2) 8.4. The Tr

ansfer Matrix and Gaussian Potentials 8.5. Transfer Matrix in the Ising Model 8.6. The Ising Ladder or Polymer 8.7. Ising Model on the Isotropic Square Lattice (2D) 8.8. The Phase Transition 8.9. A Question of Long-Range Order 8.10. Ising Model in 2D and 3D 8.11. Antiferromagnetism and Frustration 8

.12. Maximal Frustration 8.13. Separable Model Spin-Glass without Frustration 8.14. Critical Phenomena and Critical Exponents 8.15. Potts Models Chapter 9 Monte Carlo and Other Computer Simulation Methods 9.1. Numerical Methods in Statistical Mechanics 9.2. Molecular Dynamics 9.3. Stochastic Proces

ses 9.4. Transition Rates and the Master Equation 9.5. Monte Carlo Moves 9.6. Applications of ARM and DOMC 9.7. Monte Carlo Estimates of Thermal Averages 9.8. Equilibration Times 9.9. Discrete Variables 9.10. Continuous Thermodynamic Functions and Histogram Methods 9.11. Phase Transitions 9.12. MC C

alculation of Critical Exponents: Finite-Size Scaling …… Chapter 10 Critical Phenomena and the Renormalization Group Chapter 11 Some Uses of Quantum Field Theory in Statistical Physics

熵大偏差和統計力學（英文版）

為了解決Gibbs free energy un的問題，作者(美)艾里斯 這樣論述：

《熵、大偏差和統計力學》是一部教程，內容上相對獨立，自成體系。書中大偏差的講述除了為這科目做出了巨大貢獻，也將統計力學的好多方面完美結合，並且很具有數學吸引力。而且作者在沒有假設讀者具有豐富的物理知識背景下講述，使得本書能夠讓更多的讀者學習理解。每章末都附有一節注解和一節問題，這100來道練習題，附有許多提示，使得本書更加易于學習理解。目次︰（第一部分）大偏差和統計力學︰大偏差導論；大偏差性質和積分漸近；大偏差和離散理想氣體；z上的鐵磁模型；zd和圓周上的磁模型；（第二部分）大偏差定理上的復雜度和證明︰復函數和legendre-fenchel變換；大偏差的隨機向量；i. i. d. 隨機變量的

2級大偏差；i. i. d. 隨機變量的3級大偏差；附錄︰概率論；ii.7中兩個定理的證明；自旋系統中無限體積測度的等價觀點；特殊gibbs自由能量的存在性。 讀者對象︰數學專業的研究生，教師和相關專業的科研人員。 preface comments on the use of this book part i: large deviations and statistical mechanics chapter i. introduction to large deviations i.1. overview i.2. large deviations f

or 1.i.d. random variables with a finite state space i.3. levels-1 and 2 for coin tossing i.4. levels-1 and 2 for i.i.d. random variables with a finite state space i.5. level-3: empirical pair measure i.6. level-3: empirical process i.7. notes i.8. problems chapter ii. large deviation pr

operty and asymptotics of integrals ii.1. introduction ii.2. levels-l, 2, and 3 large deviations for i.i.d. random vectors ii.3. the definition of large deviation property ii.4. statement of large deviation properties for levels-l, 2, and 3 ii.5. contraction principles ii.6. large deviat

ion property for random vectors and exponential convergence ii.7. varadhan﹀s theorem on the asymptotics of integrals ii.8. notes ii.9. problems chapter iii. large deviations and the discrete ideal gas iii.1. introduction iii.2. physics prelude: thermodynamics iii.3. the discrete ideal ga

s and the microcanonical ensemble iii.4. thermodynamic limit, exponential convergence, and equilibrium values iii.5. the maxweli-boltzmann distribution and temperature iii.6. the canonical ensemble and its equivalence with the microcanonical ensemble iii.7. a derivation of a thermodynamic eq

uation ill.8. the gibbs variational formula and principle iii.9. notes iii. 10. problems chapter iv. ferromagnetic models on z iv.1. introduction iv.2. an overview of ferromagnetic models iv.3. finite-volume gibbs states on 77 iv.4. spontaneous magnetization for the curie-weiss model

iv.5. spontaneous magnetization for general ferromagnets on iv.6. infinite-volume gibbs states and phase transitions iv.7. the gibbs variational formula and principle iv.8. notes iv.9. problems chapter v. magnetic models on 7/d and on the circle v.1. introduction v.2. finite-volume gibb

s states on zd, d ≧ 1 v.3. moment inequalities v.4. properties of the magnetization and the gibbs free energy v.5. spontaneous magnetization on z, d ≧ 2, via the peierls argument v.6. infinite-volume gibbs states and phase transitions v.7. infinite-volume gibbs states and the central limit

theorem v.8. critical phenomena and the breakdown of the central limit theorem v.9. three faces of the curie-weiss model v. 10. the circle model and random waves v.11. a postscript on magnetic models v.12. notes v.13. problems part ii: convexity and proofs of large deviation theorems ch

apter vi. convex functions and the legendre-fenchel transform vii.1. introduction vi.2. basic definitions vi.3. properties of convex functions vi.4. a one-dimensional example pf the legendre-fenchel transform vi.5. the legendre-fenchel transform for convex functions on ra vi.6. notes v

i.7. problems chapter vii. large deviations for random vectors vii. i. statement of results vii.2. properties of i vii.3. proof of the large deviation bounds for d = 1 vii.4. proof of the large deviation bounds for d≧ 1 vii.5. level-i large deviations for i.i.d. random vectors vii.6. exp

onential convergence and proof of theorem ii.6.3 vii.7. notes vii.8. problems chapter viii. level-2 large deviations for i.i.d. random vectors viii. 1. introduction viii.2. the level-2 large deviation theorem viii.3. the contraction principle relating levels-i and 2 (d = 1) viii.4. the c

ontraction principle relating levels-1 and 2 (d ≧ 2) viii.5. notes viii.6. problems chapter ix. level-3 large deviations for i.i.d. random vectors ix. 1. statement of results ix.2. properties of the level-3 entropy function ix.3. contraction principles ix.4. proof of the level-3 large de

viation bounds ix.5. notes ix.6. problems appendices appendix a: probability a.1. introduction a.2. measurability a.3. product spaces a.4. probability measures and expectation a.5. convergence of random vectors a.6. conditional expectation, conditional probability, and regular condit

ional distribution a.7. the koimogorov existence theorem a.8. weak convergence of probability measures on a metric space a.9. the space ms((rd)z) and the ergodic theorem a.10. n-dependent markov chains a.11. probability measures on the space { 1, - 1}zd appendix b: proofs of two theorems i

n section ii.7 b.i. proof of theorem ii.7.1 b.2. proof of theorem ii.7.2 appendix c: equivalent notions of infinite-volume measures for spin systems c.i. introduction c.2. two-body interactions and infinite-volume gibbs states c.3. many-body interactions and infinite-volume gibbs states

c.4. dlr states c.5. the gibbs variational formula and principle c.6. solution of the gibbs variational formula for finite-range interactions on z appendix d: existence of the specific gibbs free energy d.1. existence along hypercubes d.2. an extension list of frequently used symbols ref

erences author index subject index

永續發展實踐的途徑選擇：高雄市與廈門市的比較

為了解決Gibbs free energy un的問題，作者殷瑞宏 這樣論述：

永續發展已經成為當代人類的重要議題，除了理論觀念的建立，如何透過策略行動來落實，更是值得思索的。而隨著人類發展的都市化程度愈高，作為人類主要活動地的城市，能否在政策規劃與實踐上融入永續的精神，攸關人類是否得以真正實現永續發展的願景。本文從近代永續發展脈絡演進的討論開始，確立永續發展的意涵方向後，再結合永續城市的觀點形塑出本文的核心宗旨：「永續發展乃是兼顧經濟、環境與社會三構面之間均衡的一種發展模式」，用於觀察台灣與中國大陸的城市發展情況（高雄市與廈門市）。研究發現，兩岸的城市規劃設計皆融合了永續發展的理念在內，但在實際執行成效與民眾的感受上，則是環境面向的表現最為突出，使其發展路徑的樣貌傾向

為生態現代化城市而非永續城市。本文認為，若要能實現符合均衡發展意涵的永續，理應將之視為一種思考工具，用於政策規劃與實際行動的基本框架。